A First Course in Abstract Algebra
With Applications 3rd Revised edition
By (author) Joseph J. Rotman
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First Course in Abstract Algebra by Joseph J. Rotman
Book DescriptionThis text introduces readers to the algebraic concepts of group and rings, providing a comprehensive discussion of theory as well as a significant number of applications for each. Number Theory: Induction; Binomial Coefficients; Greatest Common Divisors; The Fundamental Theorem of Arithmetic Congruences; Dates and Days. Groups I: Some Set Theory; Permutations; Groups; Subgroups and Lagrange's Theorem; Homomorphisms; Quotient Groups; Group Actions; Counting with Groups. Commutative Rings I: First Properties; Fields; Polynomials; Homomorphisms; Greatest Common Divisors; Unique Factorization; Irreducibility; Quotient Rings and Finite Fields; Officers, Magic, Fertilizer, and Horizons. Linear Algebra: Vector Spaces; Euclidean Constructions; Linear Transformations; Determinants; Codes; Canonical Forms. Fields: Classical Formulas; Insolvability of the General Quintic; Epilog. Groups II: Finite Abelian Groups; The Sylow Theorems; Ornamental Symmetry. Commutative Rings III: Prime Ideals and Maximal Ideals; Unique Factorization; Noetherian Rings; Varieties; Grobner Bases. For all readers interested in abstract algebra."
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Book DetailsISBN: 9780131862678
(243mm x 185mm x 30mm)
Imprint: Pearson Education (US)
Publisher: Pearson Education (US)
Publish Date: 28-Sep-2005
Country of Publication: United States
Books By Author Joseph J. Rotman
Learning Modern Algebra, Hardback (January 2015)
A guide to modern algebra for mathematics teachers. It makes explicit connections between abstract algebra and high-school mathematics.
Introduction to Homological Algebra, Paperback (October 2008)» View all books by Joseph J. Rotman
A fully updated edition of Rotman's easy-to-follow, step-by-step guide to the subject. The book gives a treatment of homological algebra which approaches the subject in terms of its origins in algebraic topology. The author has included material about homotopical algebra, alias K-theory.
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